What is the difference between meta-learning and zero-shot learning?
First see the definition of meta-learning:


  Meta-learning is a subfield of machine learning where automatic learning algorithms are applied to metadata about machine learning experiments. As of 2017 the term had not found a standard interpretation, however the main goal is to use such metadata to understand how automatic learning can become flexible in solving learning problems, hence to improve the performance of existing learning algorithms or to learn (induce) the learning algorithm itself, hence the alternative term learning to learn.


and zero-shot learning:


  Zero-shot learning is being able to solve a task despite not having received any training examples of that task. For a concrete example, imagine recognizing a category of object in photos without ever having seen a photo of that kind of object before. If you've read a very detailed description of a cat, you might be able to tell what a cat is in a photograph the first time you see it.


As you can see, these are different but meta-learning can be used in zero-shot learning to work better. For example see this article, as an instance.